A387058 Lexicographically earliest sequence of distinct nonnegative integers such that each term is a square number or belongs to a run of two consecutive terms summing to a square number.

0, 1, 2, 7, 3, 6, 4, 5, 8, 17, 9, 10, 15, 11, 14, 12, 13, 16, 18, 31, 19, 30, 20, 29, 21, 28, 22, 27, 23, 26, 24, 25, 32, 49, 33, 48, 34, 47, 35, 46, 36, 37, 44, 38, 43, 39, 42, 40, 41, 45, 55, 50, 71, 51, 70, 52, 69, 53, 68, 54, 67, 56, 65, 57, 64, 58, 63, 59

Offset

0,3

Comments

This sequence is a permutation of the nonnegative as each term belongs to a run of one or two terms summing to a square number, and after such a run we can extend the sequence with the least missing value.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Example

The first terms and corresponding square numbers are:
  n   a(n)  Squares
  --  ----  -----------------------------
   0     0  a(0) = 0^2
   1     1  a(0) + a(1) = 1^2, a(1) = 1^2
   2     2  a(2) + a(3) = 3^2
   3     7  a(2) + a(3) = 3^2
   4     3  a(4) + a(5) = 3^2
   5     6  a(4) + a(5) = 3^2
   6     4  a(6) = 2^2, a(6) + a(7) = 3^2
   7     5  a(6) + a(7) = 3^2
   8     8  a(8) + a(9) = 5^2
   9    17  a(8) + a(9) = 5^2
  10     9  a(10) = 3^2
  11    10  a(11) + a(12) = 5^2
  12    15  a(11) + a(12) = 5^2
  13    11  a(13) + a(14) = 5^2
  14    14  a(13) + a(14) = 5^2
  15    12  a(15) + a(16) = 5^2
  16    13  a(15) + a(16) = 5^2
  17    16  a(17) = 4^2

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A034175, A387059 (inverse).

Sequence in context: A390630 A104957 A329333 * A377483 A083119 A246163

Adjacent sequences: A387055 A387056 A387057 * A387059 A387060 A387061

Keyword

nonn

Author

Rémy Sigrist, Aug 15 2025

Status

approved